The HCS for a freely cooling gas is found by taking all the spatial
derivatives in the hydrodynamic equations equal to zero, leaving just
one equation for the temperature. The remaining fields – density and
velocity in each component – remaining homogeneous and constant:
\(\nu = \nu _0, ~ \vec{u} = 0\)  . Knowing that \(\hat{\gamma }\propto \sqrt{T}\) , and rescaling time, the result is directly
Eq. (REF ). This solution to the simplified
system of equations is what Haff derived from simple mechanical
arguments in his seminal paper [1]}.
